Nuprl Lemma : exp_zero_q
∀[e:ℚ]. (e ↑ 0 = 1 ∈ ℚ)
Proof
Definitions occuring in Statement :
qexp: r ↑ n,
rationals: ℚ,
uall: ∀[x:A]. B[x],
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
qexp: r ↑ n,
has-value: (a)↓,
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
nat_plus: ℕ+,
top: Top,
mk-rational: mk-rational(a;b),
rationals: ℚ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
b-union: A ⋃ B,
tunion: ⋃x:A.B[x],
ifthenelse: if b then t else f fi ,
bfalse: ff,
int_nzero: ℤ-o,
true: True,
nequal: a ≠ b ∈ T ,
sq_type: SQType(T),
guard: {T},
pi2: snd(t),
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
qeq: qeq(r;s),
callbyvalueall: callbyvalueall,
evalall: evalall(t),
btrue: tt,
eq_int: (i =z j),
assert: ↑b
Lemmas referenced :
value-type-has-value,
int-value-type,
qrep_wf,
nat_plus_wf,
equal_wf,
rationals_wf,
false_wf,
le_wf,
exp0_lemma,
exp-fastexp,
quotient-member-eq,
b-union_wf,
int_nzero_wf,
equal-wf-T-base,
bool_wf,
qeq_wf,
qeq-equiv,
bfalse_wf,
subtype_base_sq,
int_subtype_base,
equal-wf-base,
true_wf,
nequal_wf,
ifthenelse_wf,
subtype_rel_b-union-left,
iff_imp_equal_bool,
qeq_wf2,
mk-rational_wf,
int-subtype-rationals,
btrue_wf,
assert-qeq,
assert_wf,
iff_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
sqequalRule,
callbyvalueReduce,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
independent_isectElimination,
hypothesis,
natural_numberEquality,
hypothesisEquality,
productEquality,
lambdaFormation,
productElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
dependent_set_memberEquality,
independent_pairFormation,
setElimination,
rename,
isect_memberEquality,
voidElimination,
voidEquality,
lambdaEquality,
baseClosed,
imageMemberEquality,
dependent_pairEquality,
independent_pairEquality,
because_Cache,
addLevel,
instantiate,
cumulativity,
universeEquality,
applyEquality,
impliesFunctionality
Latex:
\mforall{}[e:\mBbbQ{}]. (e \muparrow{} 0 = 1)
Date html generated:
2018_05_21-PM-11_59_11
Last ObjectModification:
2017_07_26-PM-06_48_32
Theory : rationals
Home
Index