Nuprl Lemma : qexp1
∀[q:ℚ]. (q ↑ 1 = q ∈ 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 :
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
true: True,
so_apply: x[s],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
q-rng-nexp: q-rng-nexp(r;n),
rng_nexp: e ↑r n,
mon_nat_op: n ⋅ e,
mul_mon_of_rng: r↓xmn,
grp_op: *,
pi2: snd(t),
pi1: fst(t),
grp_id: e,
qrng: <ℚ+*>,
rng_times: *,
rng_one: 1,
nat_op: n x(op;id) e,
itop: Π(op,id) lb ≤ i < ub. E[i],
ycomb: Y,
lt_int: i <z j,
infix_ap: x f y,
subtract: n - m,
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff
Lemmas referenced :
uall_wf,
squash_wf,
true_wf,
rationals_wf,
equal_wf,
qexp-eq-q-rng-nexp,
false_wf,
le_wf,
iff_weakening_equal,
qmul_one_qrng
Rules used in proof :
cut,
applyEquality,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
introduction,
extract_by_obid,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality,
sqequalRule,
because_Cache,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination,
isect_memberFormation
Latex:
\mforall{}[q:\mBbbQ{}]. (q \muparrow{} 1 = q)
Date html generated:
2018_05_22-AM-00_00_46
Last ObjectModification:
2017_07_26-PM-06_49_37
Theory : rationals
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