Nuprl Lemma : infinite-tree_wf
∀A:(𝔹 List) ⟶ ℙ. (infinite-tree(A) ∈ ℙ)
Proof
Definitions occuring in Statement :
infinite-tree: infinite-tree(A),
list: T List,
bool: 𝔹,
prop: ℙ,
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
infinite-tree: infinite-tree(A),
prop: ℙ,
and: P ∧ Q,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
so_apply: x[s],
nat: ℕ,
exists: ∃x:A. B[x]
Lemmas referenced :
all_wf,
list_wf,
bool_wf,
iseg_wf,
nat_wf,
exists_wf,
equal_wf,
length_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
productEquality,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
because_Cache,
functionEquality,
hypothesisEquality,
applyEquality,
functionExtensionality,
universeEquality,
intEquality,
setElimination,
rename,
cumulativity
Latex:
\mforall{}A:(\mBbbB{} List) {}\mrightarrow{} \mBbbP{}. (infinite-tree(A) \mmember{} \mBbbP{})
Date html generated:
2017_04_17-AM-09_39_03
Last ObjectModification:
2017_02_27-PM-05_35_06
Theory : fan-theorem
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