Nuprl Lemma : compose-tuple-recodings_wf
∀[r1,r2:TupleRecoding]. (r2 o r1 ∈ TupleRecoding)
Proof
Definitions occuring in Statement :
compose-tuple-recodings: r2 o r1,
tuple-recoding: TupleRecoding,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
compose-tuple-recodings: r2 o r1,
tuple-recoding: TupleRecoding,
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
spreadn: spread3,
compose: f o g,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
list_wf,
tuple-type_wf,
all_wf,
equal_wf,
compose_wf,
squash_wf,
true_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
applyEquality,
functionExtensionality,
hypothesisEquality,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
universeEquality,
hypothesis,
productEquality,
cumulativity,
functionEquality,
setEquality,
lambdaFormation,
productElimination,
dependent_pairEquality,
because_Cache,
dependent_set_memberEquality,
setElimination,
rename,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality,
imageElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination
Latex:
\mforall{}[r1,r2:TupleRecoding]. (r2 o r1 \mmember{} TupleRecoding)
Date html generated:
2018_05_21-PM-08_03_56
Last ObjectModification:
2017_07_26-PM-05_40_01
Theory : general
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