Nuprl Lemma : order-type-less_wf
order-type-less() ∈ WFO{i:l}() ⟶ WFO{i:l}() ⟶ ℙ'
Proof
Definitions occuring in Statement :
WFO: WFO{i:l}(),
order-type-less: order-type-less(),
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
WFO: WFO{i:l}(),
order-type-less: order-type-less(),
member: t ∈ T,
spreadn: spread3,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
infix_ap: x f y,
so_apply: x[s],
all: ∀x:A. B[x],
subtype_rel: A ⊆r B
Lemmas referenced :
exists_wf,
order-preserving_wf,
infix_ap_wf,
all_wf,
DCC_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalRule,
lambdaEquality,
productElimination,
thin,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
functionEquality,
cumulativity,
hypothesisEquality,
productEquality,
because_Cache,
instantiate,
universeEquality,
hypothesis,
applyEquality
Latex:
order-type-less() \mmember{} WFO\{i:l\}() {}\mrightarrow{} WFO\{i:l\}() {}\mrightarrow{} \mBbbP{}'
Date html generated:
2016_05_15-PM-04_13_32
Last ObjectModification:
2015_12_27-PM-02_59_30
Theory : general
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