Nuprl Lemma : ocmon_subtype_omon
OCMon ⊆r OMon
Proof
Definitions occuring in Statement :
ocmon: OCMon,
omon: OMon,
subtype_rel: A ⊆r B
Definitions unfolded in proof :
ocmon: OCMon,
omon: OMon,
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
abmonoid: AbMon,
mon: Mon,
so_lambda: λ2x y.t[x; y],
infix_ap: x f y,
so_apply: x[s1;s2],
so_apply: x[s],
uimplies: b supposing a,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
cand: A c∧ B
Lemmas referenced :
subtype_rel_sets,
abmonoid_wf,
ulinorder_wf,
grp_car_wf,
assert_wf,
grp_le_wf,
equal_wf,
bool_wf,
grp_eq_wf,
band_wf,
cancel_wf,
grp_op_wf,
uall_wf,
monot_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
because_Cache,
lambdaEquality,
productEquality,
cumulativity,
setElimination,
rename,
hypothesisEquality,
applyEquality,
functionEquality,
independent_isectElimination,
setEquality,
lambdaFormation,
productElimination,
independent_pairFormation
Latex:
OCMon \msubseteq{}r OMon
Date html generated:
2018_05_21-PM-03_14_01
Last ObjectModification:
2018_05_19-AM-08_24_48
Theory : groups_1
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