Nuprl Lemma : flip_twice
∀[k:ℤ]. ∀[x,y,i:ℕk]. (((y, x) ((y, x) i)) = i ∈ ℤ)
Proof
Definitions occuring in Statement :
flip: (i, j),
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
apply: f a,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
compose: f o g,
int_seg: {i..j-},
true: True,
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
int_seg_wf,
equal_wf,
squash_wf,
true_wf,
flip_inverse,
subtype_rel_self,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
hypothesis,
Error :inhabitedIsType,
hypothesisEquality,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
axiomEquality,
extract_by_obid,
natural_numberEquality,
because_Cache,
Error :universeIsType,
intEquality,
setElimination,
rename,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
imageMemberEquality,
baseClosed,
instantiate,
independent_isectElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}[k:\mBbbZ{}]. \mforall{}[x,y,i:\mBbbN{}k]. (((y, x) ((y, x) i)) = i)
Date html generated:
2019_06_20-PM-01_36_14
Last ObjectModification:
2018_09_26-PM-05_52_32
Theory : list_1
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