Nuprl Lemma : qeq_refl
∀[r:ℤ ⋃ (ℤ × ℤ-o)]. qeq(r;r) = tt
Proof
Definitions occuring in Statement :
qeq: qeq(r;s),
int_nzero: ℤ-o,
b-union: A ⋃ B,
btrue: tt,
bool: 𝔹,
uall: ∀[x:A]. B[x],
product: x:A × B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
qeq: qeq(r;s),
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
all: ∀x:A. B[x],
int_nzero: ℤ-o,
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a),
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
b-union: A ⋃ B,
tunion: ⋃x:A.B[x],
bool: 𝔹,
unit: Unit,
ifthenelse: if b then t else f fi ,
pi2: snd(t),
btrue: tt,
bfalse: ff
Lemmas referenced :
valueall-type-has-valueall,
b-union_wf,
int_nzero_wf,
bunion-valueall-type,
int-valueall-type,
product-valueall-type,
set-valueall-type,
nequal_wf,
evalall-reduce,
equal_wf,
squash_wf,
true_wf,
bool_wf,
eq_int_eq_true,
btrue_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
sqequalRule,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
productEquality,
hypothesis,
independent_isectElimination,
because_Cache,
lambdaEquality,
independent_functionElimination,
lambdaFormation,
hypothesisEquality,
natural_numberEquality,
callbyvalueReduce,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
imageMemberEquality,
baseClosed,
productElimination,
multiplyEquality,
setElimination,
rename,
unionElimination,
equalityElimination,
isintReduceTrue
Latex:
\mforall{}[r:\mBbbZ{} \mcup{} (\mBbbZ{} \mtimes{} \mBbbZ{}\msupminus{}\msupzero{})]. qeq(r;r) = tt
Date html generated:
2018_05_21-PM-11_43_38
Last ObjectModification:
2017_07_26-PM-06_42_55
Theory : rationals
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